Anti-Szego quadrature rules

Kim, Sun-Mi; Reichel, Lothar

doi:10.1090/S0025-5718-06-01904-1

Anti-Szego quadrature rules
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by Sun-Mi Kim and Lothar Reichel PDF

Math. Comp. 76 (2007), 795-810 Request permission

Abstract:

Szegő quadrature rules are discretization methods for approximating integrals of the form $\int _{-\pi }^{\pi } f(e^{it}) d\mu (t)$. This paper presents a new class of discretization methods, which we refer to as anti-Szegő quadrature rules. Anti-Szegő rules can be used to estimate the error in Szegő quadrature rules: under suitable conditions, pairs of associated Szegő and anti-Szegő quadrature rules provide upper and lower bounds for the value of the given integral. The construction of anti-Szegő quadrature rules is almost identical to that of Szegő quadrature rules in that pairs of associated Szegő and anti-Szegő rules differ only in the choice of a parameter of unit modulus. Several examples of Szegő and anti-Szegő quadrature rule pairs are presented.

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